In Thrust We Trust

Fuel efficiency or raw power?  This article explains what a rocket needs to get into orbit.

In Thrust We Trust

Launch vehicle design encompasses multiple challenges – one of which is the need to accelerate a payload to such a velocity as to achieve a stand-off with the Earth’s gravity.  This stand-off is reached when the payload has reached about 7.6 km/s relative to the ground and is equal to the orbital velocity required to maintain station at the notional altitude of the International Space Station. This number is on the low side when you consider the speed lost fighting gravity and the atmosphere.  The real velocity needed to reach orbit is over 9.0 km/s.

However, once you’re there, if you actually want to go anywhere but low Earth orbit,  you’re going to need even more velocity.  The chart below shows the velocities required to reach several popular orbits or intermediary trajectories used to transfer spacecraft from one orbital type to another.

orbital-delta-v-map

As the diagram clearly shows, the majority of the necessary velocity a spacecraft must acquire to go anywhere in space is dominated by the amount of energy required just getting to the ISS’s altitude.  As Heinlein famously said, once you’re in orbit, you’re halfway to anywhere.  This rings true especially when you consider that the true measure of space is not units of distance (km) but in velocities (km/s).

Driving down the highway on a car, you can travel many thousands of kilometers to reach your destination.  In space, however, you can travel many millions of kilometers in orbit and not go anywhere, effectively. The only way to get to a new location is to stomp on the accelerator and apply a generous helping of deltaV to the situation.  This speed will change your orbit and allow you go other places within the solar system.

In many ways, the launch phase of a space vehicle’s travel is the most challenging.

For every kilogram of payload to be launched into orbit, roughly 10 kg of fuel will need to be expended to get it there.  So the engines of the first stage must be able to lift at least 11x times the mass of the payload just to carry enough fuel to finish the job.  And this is neglecting the mass of any upper stages and the mass of the engines themselves which increase the required thrust dramatically.

Additionally, during the boost phase of a launch, the atmosphere fiercely resists the acceleration of the rocket in the form of drag.  Then you must also account for the ‘drag’ caused by gravity – the Earth is continuously pulling the rocket at 9.8 m/s back toward the ground.  What does this mean?

Well it means that for the first part of the launch you want raw horsepower behind your rocket, not gas-sipping fuel efficiency.

All of the thrust produced by the lower stages push the payload closer and closer to that speed while fighting against the forces of drag and gravity that pulls the rocket toward an abrupt meeting with the ground.  The longer it takes to reach this velocity, the more fuel that the rocket is burning, which means you have to bring more fuel to continue firing the engines and then yet more fuel to allow you to lift that fuel.  It’s a vicious cycle and one that can be overcome with raw power.

Analogy time

cropped-dragster
Which will get you to orbit for less fuel – this behemoth or a gas bill-friendly commuter car?

Imagine two cars hitched to a pulling winch with a tow cable of infinite length.  Now even though the cable of this winch is of infinite length, it can only be reeled out of the spool at a set speed.  Above that speed, the cable begins to stretch until it eventually snaps, setting the cars free to continue their journey.

OLYMPUS DIGITAL CAMERA
This is gravity. Basically.

One of the cars is a hybrid commuter, a perfect car keeping your gas bill low after the daily 20-mile trek to work.  The other car in this scenario is a drag racer, a gas-guzzling, high-horsepower machine that can put out massive amounts of torque if only you can afford to keep it in gas and tires.

It seems obvious that if you had to pick one of these cars to break free of the winch, you’d want to be driving the dragster.  The hybrid commuter can travel great distances using much less fuel than the dragster but it takes a very long time for this low-powered vehicle to reach the required speed to break the cable.  It just doesn’t have the raw power required for the job at hand.  The muscle car, however, has little trouble launching forward against the winch and soon gets going fast enough to snap the cable.

That cable is gravity, air drag and the mass of the rocket itself working against it on its journey to space.  The speed at which the cable snaps at is orbital velocity – until you reach that speed the cable will keep reeling out to infinite length and tug on the car the whole way. These imaginary cars can’t escape the winch until they snap the cable and rockets cannot escape the Earth until they reach orbital velocity.

This explains to a great extent why most rockets have very powerful, if inefficient, first stages.  The F-1 engines on the Saturn V were terrible gas guzzlers – and to illustrate this point, I propose using a novel unit of measure, the “swimming pool”.  As the chart below illustrates, it took the five F-1 engines on the Saturn V first stage a little less than 5 seconds to drain the mass of the average back-yard swimming pool.

swimming-pools-over-time

…it took the five F-1 engines on the Saturn V first stage a little less than 5 seconds to drain the mass of the average back-yard swimming pool.

And they did this relatively inefficiently, too boot.  The equivalent to a miles per gallon rating for rocket engines is the specific impulse, measured in seconds.  As with miles per gallon, higher numbers are better, so you want your rocket to have a high specific impulse. F-1’s could only manage 263s of specific impulse at sea level, which is low as liquid rocket engines go.  Despite this, however, the engines did the important job of chucking the massive stack above it high into the atmosphere and with enough starting speed for the lower thrust, higher-efficiency upper stage engines to finish the job.

The Space Shuttle and the Ariane V use even less efficient engines to do most of the lifting early in flight.  Both of these rockets use highly efficient Hydrogen/Oxygen engines at lift-off, but the vast majority of the thrust being provided to the launch the stack is in fact from the solid rocket motors strapped to the side.  It’s only after these large boosters have been jettisoned that the main engines on the rocket itself take over as the main impulsive force.  And it’s a good thing too that these engines should take over – the solid rocket motors only manage 238s s in specific impulse at sea level while Space Shuttle’s main engines and the Ariane 5’s Vulcain engines achieve over 400s.

Back to the car analogy

Imagine now that both of the cars have managed to snap the cable on the winch that was reeling them back. They are now free to continue driving and the dragster, having snapped its cable far faster, pulls ahead with a commanding lead.  The hybrid commuter follows but with its low horsepower engine, it can’t close the gap.  If you let this thought experiment ramble on, you’ll realize that eventually these cars are going to run out of gas.

Somewhere down the highway, the dragster owner pulls off to the shoulder to let the hybrid commuter pass.  Free from the winch, the hybrid commuter uses its lower horsepower (but far more efficient) engine take it further on a single tank of gas than the dragster could manage.  Neither car is ‘better’ than the other; they are both designed for different purposes.  The dgraster has the power to let people live out their speed demon fantasies while the commuter car lets people make it to and from work at minimal cost.

Thus it is with rocket engines: different engines for different tasks.  The major difference here is that the rocket stack should ideally be capable of both jobs, high thrust and high efficiency as their path to orbit require them each in turn.

For example, once a rocket is nearly free from the atmosphere and has attained enough forward and upward velocity, it can afford to take longer to continue accelerating to orbit.  At this stage of the flight, you really prefer to use a more efficient engine at the cost of lower thrust to deliver a larger payload to orbit than you could otherwise lift.  For this reason, most rocket stacks do use different engines for different regimes in their flight path through the use of staging.

As pointed out, the Space Shuttle and Ariane V use both low-efficiency, high-thrust boosters and low-thrust, high efficiency engines.  The Saturn V was similar in that while the five F-1’s under the first stage were gas-guzzling behemoths, the 2nd and 3rd stages used the same high ‘miles per gallon’ fuels of Hydrogen and Oxygen as the Space Shuttle and Ariane V main stages.

This doesn’t cover all scenarios, of course.  Different engines for different tasks means that some rockets wind up with upper stages that are used in space that are even less efficient than the first stage of the rocket.  This, however, has much more to do with the attributes of the different types of propellants that feed these engines rather than thrust versus efficiency concerns.  There are many other practical concerns that drive engineers to make design choices that seem counter-intuitive on paper but turn out to be the proper solution for the problem at hand.

One of these practical concerns is the densities of the fuel that is being used.  Burning Hydrogen with Oxygen will provide the highest practical fuel efficiency for a rocket engine.  But Hydrogen is not dense and requires a much larger tank to store it than a tank for an equal-mass portion of other rocket propellants such as Kerosene.  This larger tank means more ‘dead mass’ that doesn’t help your rocket get to orbit which means you must carry more fuel (and thus have an even bigger tank) just to carry the larger tank volume in the first place.  In some cases, minimizing the overall size of the rocket can offset the performance penalty

Rocket engines are happy when they’re drowning in fuel and to keep them supplied, various types of turbo pumps gulp and condense the fuel and oxidizer delivered to the engines.  However, there is a practical limit to how fast you can condense and pump these fluids.  As the compressor blades in these turbo pumps spin faster, the differential in fluid pressure on the inner and outer surface of the blades grows larger. Eventually, the pressure drops so low on one side of the pump blades that the fuel or oxidizer begins to boil and form vacuum pockets.  This is a tricky phenomenon that I’ll try and explain –

From cars to cooking

2008-07-05_water_boiling_in_cooking_pot
Come back in an hour and this water will still be 100 C.

Have you ever noticed that cooking instructions on food packaging states that at higher altitudes, foods need to cook longer?  This is because the lower pressure at altitude makes the water boil at a lower temperature than it does at sea level.  And because water always stays the same temperature while boiling (i.e. you can boil water forever and it won’t ever get hotter), this means your food is going to take longer to cook.

This sort of thing happens in turbo pumps and it is called cavitaion.  When the fluid behind the pump reaches a low enough pressure, it begins to boil at low temperatures, just like your macaroni and cheese noodles while you’re in Colorado.

cavitacion
Cavitation on propeller blade in water

The bubbles that form are mostly empty space and when they collapse, a lot of energy is added to the fluid and objects around them.  You can think of it like microscopic bombs going off, pitting and damaging the metal turbo pump blades.  Obviously, as this goes on, the blades begin to wear and work less efficiently until they fail by exploding themselves all over the critical engine hardware surrounding them.

Orbital Sciences Antares Launch

When this happens, your rocket is going to have a bad time. This Antares rocket was taken down by an oxygen turbine pump failure.

So for highly efficient but low-density propellants, you really need to be able move as much fuel as you can without blowing up your turbo pumps.  This is done by either staging the turbo pump cycle or lowering the thrust.

Staging your turbo pump cycle is a nice way to beat the physics of cavitation.  In these systems, each compressor set lowers the pressure by a little bit before passing it on to the next set that lowers it a little more.  In this case, the change in pressure is kept smaller for any particular stage so the likelihood that propellant on the other side will begin to cavitate is low.

This comes at the cost of vastly increasing the complexity, cost and mass of your system.  Obviously, none of these things are good for rocket engineering but this is the trade you work with if you want highly-efficient and high-thrust rocket engines.  The other approach is to just pump less fuel, which helps to manage pressure levels in the turbo pumps.  However, this means you can’t thrust very high because the engines don’t have a lot of fuel to work with.  To make matters worse, the lower your thrust, the smaller your overall rocket will have to be to allow the engines to still lift it off the pad.

On the other hand, Kerosene and a few other (lower efficiency) propellants are much denser so for a given pump size you can provide much more fuel to the engines without blowing them up.  Additionally, because the propellants are denser, this means your propellant tanks can be smaller – allowing you to add even more mass or more velocity to the payload.

Once free of the atmosphere and further out of the gravity well, however, you can tolerate the lower accelerations caused by low thrust, high efficiency engines and so it makes sense to use different engines at this point through staging to maximize your overall payload.  Some satellites even take this principle to an extreme by utilizing propellant and engine types with an order of magnitude higher efficiency and many orders of magnitude lower thrust.  These engines produce the thrust equivalent of a piece of paper falling on your hand but provide an efficiency level on the order of 1000s or higher specific impulse.

This trade-off between thrust and efficiency thus dominates the engineering trade space for launch vehicles.  It has led to many uniquely awesome solutions to the problem of throwing mass into orbit.  The upcoming article Exotic Propellants will follow up on some of the other practical concerns behind propellant choice and rocket engine types.

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